Almost anywhere you eat will be good in NYC. If they dont have good food they will die quick in NY.
You can bike it, just be careful. Most walk, cab or use the subway. Cabs are dirt cheap. They also have the guys on bikes that ride you around the city. Manhattan is busy, busy. The Soho and Tribeca area are more quiet. Some beautiful places in Brooklyn. They have a spot down near the water to take a nice bike ride in Brooklyn.
It will be a whole different world in NYC as its the city that never sleeps!
You have to visit the Museum of Sex.
When are you coming? I'll be there a bit in April.